Robust Train Timetabling Problem: Mathematical Model and Branch and Bound Algorithm

This paper illustrates the results of an investigation into developing a new robust train-timetabling problem in a single-track railway line. The proposed model is formulated as a robust form of the mixed integer approach. A branch-and-bound (B&B) algorithm, along with a new heuristic beam search (BS) algorithm, is presented to solve the model for large-scale problems in reasonable time. We also propose two different methods to measure the required buffer times under the assumption of unknown and known distribution functions of disturbances. We have generated some random instances, and the efficiency of the B&B and BS algorithms are demonstrated by comparing the results with common software packages as well as a new lower bound method. The results demonstrate that the B&B algorithm can find optimum solutions in a shorter amount of time compared with common software packages such as Lingo. Moreover, the BS algorithm can effectively find a near-optimum solution in a rational amount of time.